An old man moves on a semi-circular track of radius 7 km during a morning walk. If he starts at one end of the truck and reaches at the other end, the distance and displacement of the person are :

Options

A. 20 km, 7 km
B. 22km, 14km
C. 14km, 7km
D. All of these

Answer

To solve the problem, we need to determine both the distance traveled by the old man on the semi-circular track and his displacement from the starting point to the endpoint.

### Step-by-Step Solution:

1. **Understanding the Track**:
The old man walks along a semi-circular track with a radius of 7 km.

2. **Calculating the Distance**:
- The distance traveled by the old man is the length of the semi-circular path.
- The formula for the circumference of a full circle is \( C = 2\pi r \).
- Since the old man is walking only half of the circle (a semi-circle), the distance \( D \) he travels is:
\[ D = \frac{1}{2} \times 2\pi r = \pi r \]
- Substituting the radius \( r = 7 \) km:
\[ D = \pi \times 7 \approx 22 \text{ km} \quad (\text{using } \pi \approx 3.14) \]

3. **Calculating the Displacement**:
- Displacement is defined as the shortest straight-line distance from the starting point to the endpoint.
- For a semi-circular path, the displacement is equal to the diameter of the circle.
- The diameter \( d \) is given by:
\[ d = 2r \]
- Substituting the radius \( r = 7 \) km:
\[ d = 2 \times 7 = 14 \text{ km} \]

4. **Final Results**:
- The distance traveled by the old man is approximately **22 km**.
- The displacement from the starting point to the endpoint is **14 km**.

### Summary:
- **Distance**: 22 km
- **Displacement**: 14 km